Do Hedge Fund Managers Possess Timing and Selectivity Skill? Evidence from Stock Holdings. Minjeong Kang

Transcription

1 Do Hedge Fund Managers Possess Timing and Selectivity Skill? Evidence from Stock Holdings by Minjeong Kang A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Approved April 10, 2013 by the Graduate Supervisory Committee: George O. Aragon, Chair Michael G. Hertzel Oliver Boguth ARIZONA STATE UNIVERSITY May 2013

2 ABSTRACT I study the performance of hedge fund managers, using quarterly stock holdings from 1995 to I use the holdings-based measure built on Ferson and Mo (2012) to decompose a manager s overall performance into stock selection and three components of timing ability: market return, volatility, and liquidity. At the aggregate level, I find that hedge fund managers have stock picking skills but no timing skills, and overall I do not find strong evidence to support their superiority. I show that the lack of abilities is driven by the large fluctuations of timing performance with market conditions. I find that conditioning information, equity capital constraints, and priority in stocks to liquidate can partly explain the weak evidence. At the individual fund level, bootstrap analysis results suggest that even top managers abilities cannot be separated from luck. Also, I find that hedge fund managers exhibit short-horizon persistence in selectivity skill. i

3 ACKNOWLEDGMENTS I thank George O. Aragon, Michael G. Hertzel, Oliver Boguth, Esben Hedegaard, Yakov Amihud, Wayne Ferson, John Griffin, Haitao Mo, Laura Linsey, Illona Babenko, Yuri Tserlukevich, Claudia Costodio, Andra Ghent, seminar participants at ASU brownbag seminar and FMA doctoral consortium. ii

4 TABLE OF CONTENTS Page LIST OF TABLES... vi LIST OF FIGURES... vii CHAPTER 1 INTRODUCTION LITERATURE PERFORMANCE MEASURE AND ESTIMATION Unconditional model Conditional model DATA RESULTS CONCLUSION REFERENCES iii

5 LIST OF TABLES Table Page 1. Factors Average fund s exposure Hedge fund managers subject to 13F filings and their stock holdings Analysis at portfolio level I Analysis at portfolio level II Capital constraints Non-long equity positions Bootstrap analysis Performance persistence iv

6 LIST OF FIGURES Figure Page 1. Cumulative traded liquidity risk factor: Pastor and Stambaugh vs. Amihud The average fund s beta Dynamics of alpha Capital constraints Non-long equity positions Distribution of individual Fund Alphas Predictability of liquidity v

7 Chapter 1 INTRODUCTION Hedge fund managers are often perceived as savvy investment managers who can exploit their capacity for stock picking and market timing abilities without much limitation in their trading strategies. To profit from these opportunities, the smartest money managers have migrated to the hedge fund industry, thereby contributing to its dramatic growth in the last two decades. 1 A large literature has developed contemporaneously to examine whether hedge fund managers truly exhibit superior ability. An important theme in this literature is the difficulty of using the available fund returns data to measure performance, due to several potential measurement biases, including self-selection, and distortions between reported and economic returns (e.g., Bollen and Pool (2009), Fung and Hsieh (2000, 2001), Getmansky, Lo, and Makarov (2004), Jiang, Yao and Yu (2007), and Liang (2000, 2003)). In response to these challenges, a more recent strand of literature studies hedge fund managers mandatory disclosures of quarterly portfolio holdings contained in Form 13F filings. 2 This approach can potentially sidestep many of the pitfalls associated with returns-based performance measures and utilize an array of weight-based measures applied extensively in other settings, like mutual funds. I study hedge fund managers performance using a large sample of quarterly holdings from 1995 to In particular, I build on Ferson and Mo (2012), who use a stochastic discount factor (SDF) approach that decomposes a manager s overall 1 According to Griffin and Xu (2009), hedge fund assets under management (AUM) have increased roughly from $38 billion in 1990 to $2.48 trillion in mid According to Section 13(f) of the Securities Exchange Act of 1934, hedge funds with over $100 million under management are required to fill out 13F forms on a quarterly basis for all U.S. equity positions worth over $200,000, or more than 100,000 shares. 1

8 performance into several components: security selection, market return timing, and market volatility timing. The three components can be expressed as a covariance between a manager s portfolio weights and idiosyncratic stock returns (stock selection), market returns (return timing), and negative market volatility (volatility timing). I extend the Ferson and Mo (2012) decomposition to address a third component of timing liquidity timing that measures the covariance between a manager s portfolio weights and market liquidity. To examine liquidity timing ability I construct a marketwide traded liquidity risk factor based on Amihud (2002). This will be discussed more in detail later. At the aggregate level, I find that the average hedge fund manager delivers overall alpha of 2.08% (t-statistic 0.45), which represents selectivity alpha of 2.41% (2.54) per year and timing alpha of -0.32% (-0.07) per year. 3 4 Although my point estimate can be economically meaningful as it covers the standard fixed management fees of 1 to 2%, the evidence is weak considering the conventional view of hedge fund managers superiority and the high incentive fees of 15 to 20%. Griffin and Xu (2009) also provide weak evidence on hedge fund managers abilities. They study hedge fund managers stock holdings using Daniel, Grinblatt, Titman, and Wermer s (DGTW, 1997) characteristicbased performance measure, and conclude that hedge fund managers do not possess superior ability. However, I also explore other dimensions of abilities such as volatility 3 For the definition of the average fund, see panel A of Table 4. 4 If I look at only Long/Short Equity Hedge Strategy (42% of the managers in my sample), the overall alpha is % per year (t-statistic -0.25), which represents selectivity alpha of 38.00% per year (2.52) and timing alpha of % (-0.61) per year. I determine a manager s investment style as the investment style which is most frequently used by its funds under management. 2

9 and liquidity timing, and more importantly, I shed additional light on why we do not find strong evidence to support the conventional view of hedge fund managers superiority. One possible explanation for the weak evidence is that the average hedge fund performance largely fluctuates over time; hence the time-series mean offsets all extremes and remains insignificant. To investigate this, I perform a year-by-year and structural breakpoint analysis, which reveals that the overall performance varies with market conditions. I find that the main determinant of the volatile performance is timing ability, which appears to be strongly pro-cyclical. In particular, during 2008 the total (timing) performance is 55.17% p.a. ( 59.06% p.a.), whereas during 2009 it is 23.83% p.a. (16.69% p.a.). This observation of hedge fund managers performance pro-cyclicality is in line with Patton (2008) who uses various different concepts of neutrality to present evidence against the market neutrality of hedge funds. 5 In a similar context, Jurek and Stafford (2012) develop a simple state-contingent framework for evaluating the cost of capital for hedge fund managers non-linear risk exposures. They use the portfolio of writing index (S&P 500) put options and holding cash, and argue that the cost of capital estimated from the traditional linear factor model cannot cover the proper required rate of capital. Thus, the weak evidence of superior ability in this paper may suggest that a holdings-based measure can account for the hedge fund managers non-linear risk exposure and impose proper cost of capital which is higher than that imposed by a 5 If I look at only Equity Market Neutral managers (8.1% of the managers in my sample), the performance is far from being market neutral. The total alpha is % (-1.77) per month and 23.01% (1.10) per month during 2008 and 2008, respectively. 3

10 returns-based model. 6 That is, a stock-level linear factor model may be able to overcome the underestimation issue of cost of capital inherent in a portfolio-level linear factor model. In fact, with a holdings-based measure we can measure a fund s beta directly, and allow a fund beta to change over time (on a monthly frequency in this paper), whereas with a returns-based measure we cannot measure a fund s exposure directly, and usually assume a constant beta over the entire sample period. The change in the average fund s performance with market conditions may not be detectable with an unconditional model. Under the conditional model in which I incorporate market conditions into the performance measure, the timing component (0.17% p.a.) becomes positive, whereas the selectivity alpha (2.39% p.a.) remains similar to its level without conditioning information. Moreover, about 20% of the overall performance during 2008 can be accounted for by conditioning information. Thus factoring economic state in the performance measure can help avoid committing the mistakes of undervaluing managers abilities. The fluctuations of the average fund s performance with market conditions may also be explained by hedge funds capital structure. It is theoretically well established that arbitrageurs reliance on outside financing limits arbitrageurs trading activities. (e.g., Shleifer and Vishney (1997), Vayanos (2004), Gromb and Vayanos (2002, 2010), Brunnermeier and Pedersen (2009)) That is, during crises, in response to the first sign of deteriorating performance, hedge fund investors and lenders will react promptly by redeeming their shares and issuing margin calls. To meet the surging redemption requests 6 For the evidence of hedge fund managers positive and statistically significant alpha based on a linear factor model and returns data, see e.g., Agarwal and Naik (2004), Fung and Hsieh (2004), and Hasanhodzic and Lo (2007). 4

11 and the heightened margin requirements, hedge funds may be forced to liquidate their positions at fire-sale prices. During market turmoil, the situation worsens because many other investors are also forced to sell off their positions at the same time. This behavior is detrimental to hedge funds performance because it prevents fund managers from implementing discretionary trading due to the widened bid-ask spread and increased leverage ratio of funds. Thus, hedge funds that allow investors to withdraw their money on short notice or rely heavily on leverage may encounter more difficulty in exploiting their superior ability when the market is tight. I show that hedge funds with strong share restrictions outperform those with weak share restrictions by 6.23% (2.95) per year during 2008, and by 2.29% (2.90) per year over the sample period. The latter is consistent with Aragon (2007) who presents the evidence of liquidity premium embedded in the share restrictions in hedge fund industry. The debt capital constraints due to leverage do not seem to affect performance as much as share restrictions. Also, given that the main determinant of the bad performance during market downturns is market return timing component, it is possible that facing forced liquidation hedge funds may prefer to sell off low market beta stocks, or that low market beta stocks happen to be those stocks subject to be liquidated first, like liquid stocks. This priority may expose hedge funds more to the market when the market return is low, causing their performance to deteriorate. This idea is similar to arguments in the previous literature which posits that there is a pecking order in stocks to sell off in the face of forced liquidation. (e.g., Ben-David, Franzoni and Moussai (2011), Brown, Carlin and Lobo (2010), and Scholes (2000) argue that investors put a higher priority on liquid stocks in the face of forced liquidation.) However, I find that they reduced their market return 5

12 exposure during crisis both by selling high beta stocks and buying low beta stocks. Also, they spent more money in buying low market beta stocks than earned by selling high market beta stocks. But, the exposure was still positive, and the market excess return was way below its historical average, which yields negative market return timing ability. In addition, we observe that the market beta of the stocks purchased by the average fund was highest during the tech bubble. In contrast, I find that the average hedge fund manager increased its exposure to the market liquidity during crisis by selling less sensitive stocks and buying more sensitive stocks. That is, they increased their exposure to the market liquidity when they were supposed to decrease. This implies their lack of liquidity timing ability. Indeed, I do not detect any significant results with respect to liquidity timing ability. In addition, consistent with prior literature the average hedge fund appears to prefer to sell off liquid stocks during market downturns. So it seems that the average hedge fund manager liquidated liquid stocks with high sensitivity to market return and low sensitivity to market liquidity. In fact, the correlation coefficients among market beta, liquidity beta, and liquidity confirm these observations. Also, although I find that the correlation coefficient between liquidity and liquidity beta of the stocks held by hedge fund managers is overall negative over the sample period, it closes to zero during crisis. This may advocate Sadka and Lou (2011) who argue that stock-level liquidity and liquidity risk (beta) are different concepts by showing that liquid stocks underperformed illiquid stocks during the recent financial crisis and that the performance of stocks during the crisis can be better explained by historical liquidity beta than stock-level liquidity. 6

13 Another possible story for the pro-cyclical movement of the average fund performance is that 13F data does not provide complete picture of all holdings, so we cannot observe their other positions which can possibly deliver positive alpha. Using funds returns data which reflect the performance from complete holdings, and 36-month rolling window, I find that the average fund exhibits positive market return timing, but negative liquidity- and volatility timing abilities during the recent financial crisis, but overall they do not appear to possess any timing abilities. In addition, the use of derivatives does not seem to be related to the time-variation of performance. Thus it is possible that during crisis, hedge funds attempted to time the market return during crisis using short positions, but it does not look like other positions are material in the average manager s performance. Although I do not find much evidence supportive of superior ability at the aggregate level, it is possible that there are some managers in the extreme of the crosssection who exhibit significantly positive performance. However, to investigate top managers, we need to rank managers according to their alphas, and consider order statistics. So our statistical inference needs to rely on the joint distribution of over 600 managers skill distributions. Moreover, hedge fund managers abilities are likely to be non-normal, correlated with each other, and heterogeneous, which makes it more difficult to impose an ex-ante parametric distribution from which fund returns are assumed to be drawn. In this situation I follow previous studies and employ a bootstrap procedure which does not rely on an ex-ante parametric distribution but on an ex-post empirical joint distribution. (e.g., Kosowski et al. (2006), Kosowski, Naik, and Teo (2007), Jiang, Yao, and Yu (2007)). I find that even top managers do not exhibit skill which can be 7

14 distinguishable from luck. This is in contrast with Kosowski, Naik, and Teo (2007), who study hedge fund performance using returns data and bootstrap and Bayesian approach, and conclude that top hedge fund performance cannot be explained by luck alone. This may suggest that the performance effect of market conditions outweighs that of randomness. Furthermore, hedge funds exhibit a short-horizon performance persistence in selectivity skill, but not long-horizon persistence. This result may be in accordance with Berk and Green s (2004) model in which the combination of managers differential ability, decreasing returns to scale, and investors rational provision of capital to funds results in zero risk-adjusted, after-fee returns to the investors. 7 Also, considering the volatile movement of performance the lack of persistence in performance is not that surprising. The main contribution of this paper is that (i) I provide several possible explanations for the weak evidence on hedge fund managers superiority by exploring the time-variation and decomposition of hedge fund managers performance, share restrictions, forced liquidation, and conditioning information, (ii) I introduce a liquidity timing ability under a holdings-based measure for the first time, and (iii) I conduct bootstrap analysis using holdings data to study the cross-section of hedge fund managers various abilities for the first time. 7 Fung et al. (2008) provide empirical evidence in support of the rational model, using fund-of-funds returns data. Also, Griffin and Xu (2009) find a lack of performance persistence with the DGTW measure using hedge fund equity holdings data during In contrast, Jagannathan, Malakhov, and Novikov (2010) find significant performance persistence among superior funds, but little evidence of persistence among inferior funds. 8

15 The remainder of the paper is organized as follows. Chapter 2 looks at the relevant literature. Chapter 3 discusses performance measure and estimation method. Chapter 4 describes the sample. Chapter 5 documents the results, and Chapter 6 concludes. 9

16 Chapter 2 LITERATURE The current article is related to three strands of literature: (i) a holdings-based performance measure, (ii) hedge fund managers ability, and (iii) performance decomposition. This paper relies on a holdings-based performance measure to investigate hedge fund managers ability. A number of empirical studies have provided a good amount of evidence that hedge fund returns data suffer from several measurement biases. Fung and Hsieh (2000) discuss a selection-, an instant history-, and survivorship bias. A selection bias occurs because only funds with good performance want to be included in a database and funds with poor performance can refuse to participate in a vendor s database. An instant history bias occurs when hedge funds come into database vendors with instant histories which usually exhibit good track records, and the database vendors backfill the hedge funds performance. Lastly, survivorship bias occurs if funds drop out of a database because of poor performance and database vendors only contain information for those hedge funds that are still operating. Getmansky, Lo, and Makarov (2004) argue that the high serial correlation in hedge fund returns is likely the outcome of liquidity exposure and smoothed returns. If funds hold illiquid securities which are not actively traded and the market prices of which are not readily available, then the reported returns of these funds appear to be smoother than the economic returns which fully reflect all the available market information about the securities, which in turn will impart a downward bias on the estimated return variance. Furthermore, Bollen and Pool (2009) find a significant discontinuity in the distribution of monthly hedge fund returns at return of 10

17 zero after controlling for database biases such as survivorship bias. By showing that this discontinuity disappears when using bi-monthly returns or three months returns before an audit, they argue that hedge fund managers temporarily distort monthly returns to avoid reporting losses. Moreover, Liang (2000, 2003) finds significant differences in reported returns of the same funds between different databases. To overcome such biases of hedge funds reported returns, several recent empirical papers examine hedge fund performance using holdings data. 8 Griffin and Xu (2009) study hedge fund managers performance using quarterly 13F holdings of hedge funds, and conclude that hedge funds exhibit no ability to time sectors or pick better stock styles and raise serious questions about the perceived superior skill of hedge fund 8 The literature notes several weaknesses in employing holdings data instead of returns data: (i) First, we have to limit our investigation to long equity positions. According to Fung and Hsieh (2006), 43% of hedge funds in the TASS database (and 32% of AUM) were invested in long/short equity strategies as of Also, 81% of hedge funds (76% of AUM) in their investigation are categorized as equity-oriented funds, i.e., convertible arbitrage, emerging market, equity market neutral, event driven, global macro, and long/short equity. Further, Aragon and Martin (2011) manually collect 13F filings and document that filings in options are a small proportion of hedge fund equity positions, although this observation is based only on the set of 13F-reportable securities and exchange-traded derivatives, which is small compared to OTC derivatives. (ii) Also, we can observe holdings on a quarterly basis. But the average quarterly turnover rate for the sample in this study is 21.9%. As the definition of turnover, I use the minimum of total buys and total sales, divided by the mean of current and lagged total equity holdings. (Brunnermeier and Nagel (2004) and Ben-David, Franzoni, and Moussawi (2011) report the average quarterly turnover in their hedge fund sample as 25% and 39.4%, respectively.) This turnover rate legitimizes the use of a quarterly snapshot of holdings data to capture the low-frequency component of hedge fund trading. By splitting the sample into terciles according to the average quarterly turnover, and forming an equally weighted portfolio of going long the top turnover funds (average quarterly turnover of 37.0%) and short the bottom funds (7.0%), I find that the turnover matters only during the tech bubble (see Figure 7). However, I acknowledge that if hedge fund managers employ the strategies of buying and selling the same stocks within a quarter, we cannot capture such an activity. (iii) Furthermore, we can observe only large managers, which are subject to 13F filings requirements. We cannot observe the long equity positions of those hedge funds that are not subject to 13F filings. To address this issue, I examine the size effect within 13F hedge fund managers by splitting the sample into terciles and quintiles according to the AUM (I aggregate the time-series average AUM across funds under a management firm). I find no significant difference in performance between the top and bottom portfolios. (iv) Finally, the holdings information is at the management firm level, not at the fund level as in mutual funds. To address this issue, I split the manager sample into terciles depending on the number of funds under a manager. I find no significant difference in overall performance between the top portfolio (the average number of funds under a manager is 14.3) and the bottom (the average number of funds under a manager is 1.0, i.e., the manager level is the same as the fund level). However, the timing alpha of the top portfolio is 0.48% p.a. (t-statistic: 1.88) lower than that of the bottom. 11

18 managers. To measure performance they rely on characteristics-matched benchmarks (DGTW), which control for size, value, and momentum effects. Brunnermeir and Nagel (2004) focus on hedge funds positions in tech stocks (high price-to-sale stocks) during the technology bubble from 1998 to 2000, and find that hedge funds were able to adjust their positions in tech stocks to capture the upturn and avoid the downturn. Using a unique dataset Aragon and Martin (2012) show that hedge fund managers long equity option positions can predict the directional and non-directional movement of the underlying stocks. Agarwal et al. (2012), and Aragon, Hertzel and Shi (2012) investigate confidential positions in 13F filings and find evidence of hedge fund managers capacity for informed trading. Although portfolio managers performance can be evaluated in various respects, the existing literature mostly focuses on a specific aspect of ability. Namely, they look at only one of the following: market return timing, market volatility timing, and stockpicking skill. The literature on timing measure stems from Treynor and Mazuy (1966) who look at the characteristic line of fund rate of return against the market return. If a manager can outguess the market, the manager will increase the portfolio sensitivity to the market (slope of the line) in anticipation of market rise and decrease in anticipation of market fall, so the characteristic line would exhibit a convex upward line. But they find that all but one of the mutual funds they investigated (57 funds) exhibit no curvature, so they conclude that managers cannot anticipate the major turns in the stock market. Henriksson and Merton (1981) investigate mutual fund managers market timing ability based on the covariance between market beta and the indicator variable for the sign of excess market return, to measure managers ability to forecast positive market excess 12

19 return. This permits them to identify the separate contributions from stock picking and market timing skills, which are mixed in the Jensen s alpha from the linear regression. Busse (1999) studies mutual fund managers ability to time market volatility considering that market volatility is persistent and so predictable and that performance measures are risk-adjusted. Using mutual funds daily returns data he shows that funds that reduce systematic risk when market volatility is high earn higher risk-adjusted returns. Jiang, Yao, and Yu (2007) investigate mutual fund managers market return timing ability using holdings data. They directly measure funds market beta as the weighted average of the betas of the individual stocks held in the portfolio, and timing ability as the covariance between fund betas at the beginning of a holdings period and the holding period market returns. They find that mutual managers can time the market, which opposes to the previous evidence of insignificant or negative market timing ability of mutual funds based on returns data. A couple of papers deal with various abilities using holdings data. Daniel, Grinblatt, Titman, and Wermers (DGTW, 1997) study mutual fund managers holdings data and develop a characteristic-based performance measure. They construct benchmarks by matching stocks held by a manger to the 125 passive portfolios of similar characteristics such as market capitalization, book-to-market ratio, and prior performance. They find evidence supportive of characteristic selectivity but no evidence of characteristic timing. Ferson and Mo (2012) develop a holdings-based performance measures which accommodate market level timing, volatility timing, and stock selectivity skills based on a stochastic discount factor approach. They find no significant evidence of investment ability in mutual fund industry. 13

20 Also, some studies use returns data to investigate various abilities. Cao et al. (2012) use hedge fund returns and Treynor and Mazuy (1966) approach of CAPM regression to explore market liquidity timing ability at the individual fund level. They find that top managers can adjust their portfolios market exposure to time market liquidity. But I do not find any evidence of liquidity timing ability in this paper. The main difference in results may be due to the fact that they assume a one-factor asset pricing model (CAPM), and measure liquidity timing ability as the covariance between market beta and liquidity risk (Pastor and Stambaugh s liquidity level factor), while I assume a two-factor model consisting of market return and market liquidity, and measure liquidity timing ability as the covariance between liquidity beta and liquidity risk. 9 Chen and Liang (2007) investigate hedge fund returns data to study the market timing ability of selfdescribed market timing managers. They propose a market timing measure which jointly evaluates market return level- and volatility timing ability by regressing fund returns on the squared Sharpe ratio of the market portfolio. They find evidence of timing ability at both the aggregate and the fund level. 9 If I use Pastor and Stambaugh (2002) traded liquidity risk factor, liquidity innovation, or liquidity level, I still do not have any significant results. 14

21 Chapter 3 PERFORMANC MEASURE AND ESTIMATION In this section, I briefly discuss the performance measure used in this paper. 10 I assume a two-factor model consisting of market excess return and traded liquidity risk. 11 That is, the benchmark portfolio is, where and represent market excess return and liquidity risk, respectively. The asset pricing model basically says that the asset price is equal to the expected value of discounted asset payoff, Ω, or in net return term, Ω 0, where is a (inter-temporal) marginal rate of substitution, also called the stochastic discount factor (SDF) at time, and,,, and Ω are, respectively, asset price, an asset payoff, return in excess of risk-free rate at time, and an information set available up to time t. In our setting the primitive assets are market excess return, liquidity risk portfolio return, and risk-free rate, so the pricing formula prices these assets. 10 For details, see Cochrane (1996, 2005), Ferson and Lin (2012), Ferson and Mo (2012), and Ferson and Schadt (1996). 11 If I use Carhart four factors along with traded Amihud liquidity risk or traded Pastor and Stambaugh (PS) liquidity risk factor, the magnitude of alpha is reduced but the overall pattern is similar. The results are available upon request. For simplicity, I develop the intuition based on a two-factor model. 15

22 Assuming a linear factor model is equivalent to representing SDF as a linear function of factors (Ross (1978), Dybvig and Ingersoll (1982), Cochrane (1996)). Therefore, assuming a two-factor pricing model, we have, (1) where is our benchmark portfolio consisting of market return and liquidity risk portfolio return, and and are market-wide parameters. Section 1 Unconditional Model If a manager possesses superior information not included in the public-information set Ω, and can take advantage of it to realize superior portfolio returns, the model does not price the fund return. Then we can define an unconditional SDF-based abnormal performance measure as 0, (2) where is the SDF and is the return of the fund in excess of a short-term Treasury bill. By restricting to an unconditional measure - that is, only a constant term is in the information set - I assume any information can be proprietary. Now consider a factor model regression for the excess returns of N underlying securities in a portfolio:,, 3 where is the 2 matrix of betas, the vector of abnormal or idiosyncratic returns, and 0. If a fund forms a portfolio using weights, then the portfolio return is given by 16

23 . 4 Note that is the weighted average of betas of individual stocks held by a fund, which represents the fund s beta to benchmark portfolio. Substituting equation (1) into the definition of alpha (2) we obtain ( ),,, ; 0,,. (5) The first term in (5) captures market return level timing through the covariance between the portfolio weights set at the beginning of a period and the subsequent factor market returns. Similarly, the second term captures liquidity timing ability. The third term relates to volatility timing through the covariation between portfolio weights and the second moment matrix of benchmark returns, which is what Grinblatt and Titman (1989, 1993) missed. 12 The last term captures selectivity skill, which is the expected value of the interaction between portfolio weights and idiosyncratic abnormal returns, and excludes the part contributable to factors, which does not appear in traditional selectivity measures. The market-wide parameters and are estimated based on the assumption that the benchmark portfolio and risk-free asset satisfy the pricing model, as shown in equations (6a) and (6b) below. For each fund, I estimate a market return timing 12 They look at the covariance between portfolio weights and the returns of securities held in a portfolio, but view it in a little different way from the prior literature. They estimate a covariance as the expected value of security return multiplied by the deviation of portfolio weight from expected weight, and they proxy the expected weight as lagged weight. By doing so, they can address survivorship bias and the critique of the impact of a benchmark portfolio on performance measure. 17

24 component denoted as, market liquidity risk timing ability, a volatility timing component, and a selectivity component. The model is estimated using the generalized method of moments (GMM, Hansen, 1982) through the following moment conditions: 1 µ µ µ µ,,,,,, 0. 6a 6b 6c 6d1 6d2 6 6 (6g) Stock betas for each risk factor and month are estimated using 60 monthly data prior to the current month, requiring at least 24 months of observations. For estimation I require each fund to have at least 15 observations, except for the yearly performance and persistence test, in which I require full 12 months of observations. I estimate the marketwide parameters using the first three equations, (6a) to (6c) subject to (6g), and then plugging the parameter estimates into to the other equations (6d1) to (6f) subject to (6g) to solve for alphas. I solve the system of equations for each fund using GMM with the Newey-West (1987) covariance matrix using three lags to account for autocorrelations and heteroskedasticity-consistent estimate of the standard error. 18

25 Section 2 Conditional Model We can incorporate the effects of conditioning information into the model by either (i) scaling the returns (Hansen and Singleton (1982)), or (ii) scaling the factors (Ferson, Kandel, and Stambaugh (1987), Harvey (1989), and Shanken (1990)). In this paper, I use the latter. 13 In this case, the SDF can be represented by a linear combination of factors with weights as linear functions of instruments that change across different information sets; the conditional mean of factors can be expressed as a linear function of instruments. That is,,, ; µ, µ, µ, µ, where, and, are market excess return and liquidity risk factor at time ; µ, and µ, are conditional expectations of market excess return and liquidity risk factor at time ;,,, µ, and µ are 1 vectors of coefficients; and Ω is a 1 vector of instruments including a constant. Now the moment condition (6g) changes so that it holds when we multiply both sides of the equation by any instrument. For example, if we have two instruments, we will have nine equations for parameter estimation and twelve equations for performance estimation. Following the previous studies (Christopherson, Ferson, and Glassman (1998), Cochrane (1996), Ferson and Mo (2012), and Ferson and Shadt (1996)), I use a collection 13 For details, see Cochrane (1996). 19

26 of public information variables that are shown to be useful for predicting security returns and risks over time: (i) the lagged three-month Treasury bill yield, (ii) the lagged dividend price ratio (iii) the lagged term spread, (iv) the lagged default return spread, and (v) a dummy variable for the month of January. 20

27 Chapter 4 DATA The information on hedge fund returns, affiliations, and characteristics are from the TASS snapshot as of April 25, Because TASS has started to collect hedge fund data since 1994, it does not include defunct funds performance information before Thus I choose the sample over the period January 1994 to December 2010 to control for the survivorship bias. I obtain the 13F filers names, their equity holdings and the holding stocks prices data from the Thomson-Reuters Institutional (13F) Holdings database. To identify 13F filers that manage hedge funds, I first create a list of nonduplicate hedge fund managers names over the sample period, where hedge fund managers are defined as either a management company or an investment company in a company type field in the TASS database. Also, I make a list of non-duplicate 13F filers names over the sample period. Then I manually match the hedge fund managers names to the 13F filers names. To address the backfilling bias, I choose the observations after the date they were added to the TASS database. In the event that a hedge fund manager is matched to multiple hedge funds and hence to multiple dates added to TASS, I choose the earliest date added to TASS for the manager. In terms of the predetermined information variables, (i) Treasury-bill rates are the 3-month Treasury bill, (ii) dividend price ratio is the ratio of 12-month moving sums of dividends paid on the S&P 500 index to the prices, (iii) the term spread is the difference between the long-term yield on government bonds and the Treasury bill, and (iv) the 21

28 default yield spread is the difference between BAA and AAA-rated corporate bond yields. 14 I retrieve individual stocks information and Carhart four factors from the CRSP. 15 I expand the quarterly holdings data to the three months in the next month to compile monthly data. In this paper I focus on a traded liquidity risk factor constructed from Amihud (2002) rather than Pastor and Stambaugh s (2003) traded liquidity risk factor. Goyenko, Holden, and Trzcinka (2009) investigate whether liquidity measures constructed from daily data can measure liquidity as well as those from intraday data. They find that Amihud (2002) measure is a good proxy for price impact, while Pastor and Stambaugh s (2003) gamma does not perform well compared to other measures. When we look at the cumulative traded liquidity risk factor over time (Figure 1), we can see little timevariations in the Pastor and Stambaugh s measure even during the crises like LTCM collapse, and tech bubble burst. 16 In contrast, we can observe a lot more variations in that of Amihud s liquidity measure. Thus, it seems that new measure based on Amihud (2002) is more appropriate to study whether or not hedge fund managers time market liquidity. To construct a market-wide traded liquidity risk factor, I follow Amihud (2002) and Acharya and Pedersen (2005). 17 First I compute individual stocks daily liquidity 14 I thank Prof. Goyal for providing the data on his website: 15 I thank Prof. Fama and Prof. French for sharing the data. 16 Note that I discuss only traded factor to compute alpha. In terms of cumulative factor, their other factors (liquidity level and liquidity innovation) seem to exhibit enough time-variation compared to their traded factor. I thank Prof. Pastor and Prof. Stambaugh for sharing the data. 17 I clean the daily stock return data in the following manner: (i) I use ordinary common shares (share code is less than 20), (ii) stocks listed on NYSE/AMEX (exchange code: 1, 2) (See Reinganum (1990) on the effects of the differences in microstructure between the NASDAQ and the NYSE on stock returns, after adjusting for size and risk. In addition, volume figures on the NASDAQ have a different meaning than those on the NYSE, because trading on the NASDAQ is done almost entirely through market makers, 22

29 measure as the negative signed ratio of absolute value of stock return to dollar volume. Then I compute the individual stocks monthly liquidity measure as the average of daily liquidity measures. The market-wide monthly liquidity level measure is computed as the value-weighted average of individual stocks monthly measures, where weight is determined by the prior month-end market capitalization. Then I obtain the monthly market-wide liquidity risk (innovation) as the residual of AR(2) process of the liquidity level using prior 60 months observations. For each month, I sort stocks into deciles according to their liquidity betas which are computed using prior 60 months observations requiring at least 24 months observations and using a regression model of stock return on market return and market liquidity risk. Finally, I compute the traded market liquidity factor as the return to the spread portfolio by buying the most sensitive portfolio and selling the least sensitivity one. Here, portfolio return is computed as the value-weighted average of returns of the stocks in the portfolio where weight is determined by the prior month-end market capitalization. The final sample contains (i) 13F filers managing hedge funds, (ii) their long equity holdings of the prior quarter-end, (iii) stock returns of the current month, (iv) stock betas for pricing factors, (v) pricing factors, and (vi) the previous month s instruments for each month. whereas on the NYSE most trading is done directly between buying and selling investors. This results in artificially higher volume figures on NASDAQ.), (iii) stocks whose number of price and volume observations within a month is at least 15, (iv) stocks whose prior month-end stock price is between $5 and $1,000 and prior month-end market capitalization exists. (v) stocks whose monthly liquidity measures lie between the 1 st and below 99 th percentiles. (vi) Also, volume is measured in $ million. Finally (vii) returns are adjusted for stock delisting to avoid survivorship bias. The last return used is either the last return available on CRSP, or the delisting return, if available. While a last return for the stock of -100% is naturally included in the study, a return of -30% is assigned if the deletion reason is coded in CRSP as 500 (reason unavailable), 520 (went to OTC), (various reasons), 574 (bankruptcy), and 584 (does not meet exchange financial guidelines). (Shumway obtains that -30% is the average delisting return, examining the OTC returns of delisted stocks.) 23

30 Chapter 5 RESULTS In panel A of Table 1, I document the summary statistics for pricing factors. In panel B, I report the estimates for the market-wide parameters using equations (6a) to (6c) subject to (6g). In panel C, I document the expected value of SDF, which is actually the inverse of the expected risk-free rate when we assume that the risk-free asset is a primitive asset in the pricing model. Table 2 presents the summary statistics of the average fund s monthly exposure to each risk, that is, the weighted average of the market beta, liquidity beta, and idiosyncratic risk of individual stocks held by the manager, where weight is determined by holdings. Panel A of Figure 2 depicts the average fund s monthly risk exposure over time. Market exposure appears to be slowly increasing over time with slight dips during the NASDAQ crash and the recent global crisis. The liquidity risk exposure has been increasing slowly since mid-2005 to hit the high in recent financial crisis. Also, the average fund slightly increased its liquidity exposure during the tech bubble burst. That is, the average manager seems to have been increasing its exposure to the market liquidity when they had to increase the most. Based on these observations, we can conjecture that managers may have market timing ability but no liquidity timing ability. Table 3 reports the summary statistics of hedge fund industry in terms of size and holdings over the sample period. From panel A of Table 3 we can observe the increase in the number of hedge funds, and those subject to 13F, which reflects the growth of the industry over the past decade. Because the number of managers during 1994 ends up 24

31 being only two in the final sample, I do not include this year in the analysis afterwards. Panel B documents the size of the equity holdings of hedge fund managers compared with CRSP total equity holdings. 18 To gauge the size of hedge funds subject to 13F, I examine the assets under management (AUM) in panel C, which shows that hedge funds subject to 13F are about two times bigger than their counterparts. Table 4 documents the performance estimates of the average hedge fund manager. Panel A of Table 4 presents a simple example showing how I construct a single representative portfolio in the current paper. To form an equally weighted portfolio, for each quarter I take the average of the positions of the individual managers, with one over the number of managers of the quarter as an equal weight; to form a value-weighted portfolio, I take the average of the positions of the individual managers, with total equity holdings of the quarter as weights. I use an equally weighted portfolio so that large funds do not dominate the overall results. Unless otherwise stated, average fund, portfolio level, and aggregate fund level refer to an equally weighted portfolio. Panel B of Table 4 reports the performance estimates from equations (6d) to (6f), subject to (6a) to (6c) and (6g) for the average fund under unconditional model. The results show that the average fund exhibits total alpha of 2.08% per year (t-statistic 0.45), which represents 18 As of 2010, the ratio of total equity holdings by hedge fund managers to CRSP total equity holdings (24.87%) seems to be larger than the findings of Griffin and Xu (2009) and Ben-David, Franzoni, and Moussai (2012), who document the figure as around 3% to 5%. This difference may be because they use a different sample period, proprietary data, or stricter filters than I do. For example, they use only those managers whose main line of operations is hedge fund business, they exclude large investment banks and prime brokers that might have internal hedge fund business, management companies for which the ratio of 13F AUM to TASS AUM exceeds 10%, and hedge funds with less than $1 million in total AUM, and they keep institutions of which more than half of their clients are classified as High Net Worth Individuals or Pooled Investment Vehicles. In fact, the number of hedge fund management firms in Griffin and Xu (2009) and Ben-David, Franzoni, and Moussai (2012) are around 300 and 100, respectively. However, the medians are similar. 25

32 2.41% (2.54) of selectivity skill and 0.32% ( 0.07) of timing ability. 19 Although it is statistically insignificant, the point estimate is economically meaningful as it can cover the standard fixed management fees of 1 to 2%. Also, note that the overall performance comes primarily from stock picking ability. The weak evidence of the average fund s capacity for informed trading is somewhat surprising considering the conventional view of hedge fund managers superiority and the high incentive fees investors are charged. One possible explanation for this weak evidence is that the average hedge fund performance is volatile over time, the time series mean of which fails to reflect such dynamics, thus producing insignificant estimates. To investigate the time-variation of performance, I look at a year-by-year performance. Yearly alpha is estimated using full 12 months observations for each year, and the GMM estimation method (6d1) to (6f) subject to (6g). I use the same marketwide parameter estimates as before, that is, those reported in Panel B of Table 1. Indeed, we can observe that the yearly alpha of the average fund fluctuates over time, as presented in Figure Also, although 75% of the years deliver positive total alpha, negative alpha years are primarily identified as having historically large plunges in the magnitude of alpha. Moreover, the latter is usually matched to significant market events, such as the NASDAQ crash and recent financial turmoil, that is, 15.70% per year, 29.14% per year, and 55.17% per year correspond respectively to the 2001, 2002, and 19 If I use the value-weighted portfolio, the magnitude of alpha is reduced but the overall pattern remains similar. The table is available upon request. 20 Remember that the estimation method here is not like that for the usual regression of fund returns on multiple factors, in which we need to ensure the number of estimates does not exceed the number of observations. Rather, the alphas here are computed independently of one another; thus we do not need to worry about the degree of freedom to the extent that we do not care about the significance level. 26

33 2008. Therefore, the yearly performance is determined mainly by the timing component, which is in turn largely affected by market conditions. To examine how performance changes with market conditions, I split the sample period into six sub-periods according to widely accepted structural break points: the period up to the collapse of Long-Term Capital Management L.P. (LTCM) and just before the tech bubble (January 1995 to September 1998), during the tech bubble (October 1998 to March 2000), the NASDAQ crash, the accounting scandal and September 11 attacks (April 2000 to October 2002), the subsequent period leading up to the mortgage crisis (November 2002 to June 2007), the recent financial crisis (July 2007 to December 2008), and the remaining period (January 2009 to December 2010). Within these periods, more patterns of the average manager s performance become manifest, as reported in Table 5. That is, market downturns are matched to significantly large negative alphas (the NASDAQ crash and the recent financial crisis, respectively, correspond to 20.02% p.a. (t-statistic 2.00) and 39.92% p.a. ( 1.72)), while market upturns or normal times are mostly matched to significant and positive alphas (the periods before the tech bubble, during the tech bubble, after the bubble crash leading up to the mortgage crisis, and after the recent crisis correspond to 4.86% p.a. (0.71), 23.38% p.a. (2.77), 12.81% p.a. 21, 22 (2.92), and % p.a. (1.26), respectively). 21 Fung et al. (2008) apply two structural breakpoints, LTCM crisis (September 1998) and the NASDAQ crash (March 2000), to their sample between 1995 and Hesse, Frank, and Gonzalez-Hermosillo (2008) identify subprime turbulence (July 2007) as the structural breakpoint. Ivashina and Sharfstein (2010) define August 2007 to July 2008 and August 2008 to December 2008 as crisis I and crisis II, respectively. To ensure enough observations in each sub-period, I combine the two into one (choosing either July 2007 or August 2007 does not make difference in the results). Also, the NASDAQ crash seems to continue until 2002 because of a series of accounting scandals and the September 11 attacks; therefore, I choose December 2002 as the end of the crash. ( 27